engUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332015-04-013270864017Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equationMina Mortazavim_mortazavi95@yahoo.com1Mohammad Mirzazadehmirzazadehs2@guilan.ac.ir2Department of Applied ferdowsi university of mashhad mashhad. IranDepatmant of Mathematics, University of Guilan‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by jacobi elliptic functions for the 1D MCGL equation are derived. Homogeneous method is a powerful method, it can be used to construct a large families of exact solutions to different nonlinear differential equations that does not involve independent variables.http://cmde.tabrizu.ac.ir/article_4017_0464648f9f5a70082b84fd3112ca2dcf.pdfExact traveling wave Solutions‎‎Modified Complex Ginzburg-Landau equation‎‎$(G'/G)$‎-‎expanson methodHomogeneous balance methodEextended F-expansion methodengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332015-04-013287984484Optimization with the time-dependent Navier-Stokes equations as constraintsMitra Vizhehmitravizheh@gmail.com1Syaed Hodjatollah Momeni-Masulehmomeni@shahed.ac.ir2Alaeddin Malekmala@modares.ac.ir3Department of Mathematics, Shahed UniversityDepartment of Mathematics, Shahed UniversityDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares UniversityIn this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the optimal control of the Navier-Stokes equations is proposed. Numerical examples are given to demonstrate the efficiency of the method.http://cmde.tabrizu.ac.ir/article_4484_0de495e641081aae07a2b511ceceb9bf.pdfOptimal Control ProblemsNavier-Stokes equationsPDE-constrained optimizationquasi-Newton algorithmfinite differenceengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332015-04-0132991004541Application of the block backward differential formula for numerical solution of Volterra integro-differential equationsSomayyeh Fazelifazeli@tabrizu.ac.ir1University of TabrizIn this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability region of orders 2, 3 and 4 are constructed which are suitable for solving stiff VIDEs.http://cmde.tabrizu.ac.ir/article_4541_07598b31f5bf268f9053f664f3870864.pdfVolterra integro-differential equationsBlock methodsBackward differential formulaengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332015-04-01321111224648Numerical solution of time-dependent foam drainage equation (FDE)Murat Gubesmgubes@kmu.edu.tr1Yildiray Keskinykeskin@selcuk.edu.tr2Galip Oturancgoturanc@selcuk.edu.tr3Karamanoglu Mehmetbey UniversitySelcuk UniversitySelcuk UniversityReduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE) with different initial conditions. We compare our method with the famous Adomian Decomposition and Laplace Decomposition Methods. The obtained results demonstrated that RDTM is a powerful tool for solving nonlinear partial differential equations (PDEs), it can be applied very easily and it has less computational work than other existing methods like Adomian decomposition and Laplace decomposition. Additionally, effectiveness and precision of RDTM solutions are shown in tables and graphically.http://cmde.tabrizu.ac.ir/article_4648_efda79e599c82bb21304dce4c2502549.pdfFoam Drainage EquationLaplace Decomposition MethodAdomian Decomposition MethodReduced Differential Transform MethodengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332015-04-01321231334649Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problemRahmat Darzir.darzi@iauneka.ac.ir1Bahram Aghelib.agheli@yahoo.com2Department of Mathematics, Neka Branch, Islamic Azad University, Neka, IranDepartment of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IranIn this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0http://cmde.tabrizu.ac.ir/article_4649_30ab2f42a41eb1f68dba3f0aab9d34fc.pdfBoundary value problemfixed point theoremPartially ordered setPositive solutionnondecreasing solutionengUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25332015-04-01321341464769Multi soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)-dimensionManjit Singhmanjitcsir@gmail.com1Yadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi SaboAs an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of associated linear problem or Lax pair are presented in straightforward manner and finally for proposed nonlinear equation, explicit one, two and three soliton solutions are also obtained.http://cmde.tabrizu.ac.ir/article_4769_c037a3bd2246ff1cd130bac4856a2745.pdfSoliton solutionsBilinear Backlund transformationsLax pairsPerturbation expansion